Pith Number

pith:FAIZ7R4G

pith:2026:FAIZ7R4GA6RRBPI4P2C7LTDMLW

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The FORSS Framework for Sample Size and Power Calculations With Win Statistics for Hierarchical Endpoints

Baoshan Zhang, Huiman X. Barnhart, Roland A. Matsouaka, Yuan Wu

The FORSS framework delivers accurate formula-based sample size and power calculations for win statistics on hierarchical endpoints.

arxiv:2605.17240 v1 · 2026-05-17 · stat.ME

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\pithnumber{FAIZ7R4GA6RRBPI4P2C7LTDMLW}

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Claims

C1strongest claim

The formula-based FORSS closely matches empirical power across a wide range of scenarios while maintaining Type I error rates near the nominal 5% level.

C2weakest assumption

That a user-specified flexible joint working distribution for the hierarchical endpoints, together with marginal treatment effects, is sufficient to generate super-samples whose plug-in estimates accurately support the analytical power and sample-size formulas.

C3one line summary

FORSS is a new formula-based super-sample framework for power and sample size calculations with win statistics on hierarchical endpoints that incorporates marginal effects and a flexible joint distribution.

References

39 extracted · 39 resolved · 0 Pith anchors

[1] Validity of composite end points in clinical trials.BMJ 2005; 330(7491): 594–596 2005 · doi:10.1136/bmj.330.7491.594

[2] WalkerHG,BrownAJ,VazIP,etal.Compositeoutcomemeasuresinhigh-impactcriticalcarerandomisedcontrolledtrials: a systematic review.Critical Care2024; 28(1): 184

[3] Key Issues in End Point Selection for Heart Failure Trials: Composite End Points.Journal of Cardiac Failure2005; 11(8): 567–575 2005 · doi:10.1016/j.cardfail.2005.08.350

[4] Problems with use of composite end points in cardiovascular trials: systematic review of randomised controlled trials.Bmj2007; 334(7597): 786

[5] doi: 10.1002/(SICI)1097-0258(19990615)18:11<1341::AID-SIM129>3.0.CO;2-7 · doi:10.1002/(sici)1097-0258(19990615)18:11

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Receipt and verification

First computed	2026-05-20T00:03:47.030345Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28119fc78607a310bd1c7e85f5cc6c5da6389bd1007f0f52560d8f1fe60700be

Aliases

arxiv: 2605.17240 · arxiv_version: 2605.17240v1 · doi: 10.48550/arxiv.2605.17240 · pith_short_12: FAIZ7R4GA6RR · pith_short_16: FAIZ7R4GA6RRBPI4 · pith_short_8: FAIZ7R4G

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FAIZ7R4GA6RRBPI4P2C7LTDMLW \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 28119fc78607a310bd1c7e85f5cc6c5da6389bd1007f0f52560d8f1fe60700be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf93b544b38957a6ab00cf4263a5a31c29404299f15e7c2de400a083fa9b4fee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-17T03:44:41Z",
    "title_canon_sha256": "f435e956955e3b7fed439e415d43f0713416806b3555986f59b370390b5ac291"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17240",
    "kind": "arxiv",
    "version": 1
  }
}